Question: If $a \div b = 2$ and $b \div c = \frac{3}{4}$, what is the value of $c \div a$? Express your answer as a common fraction.
Since $\dfrac{b}{a} \cdot \dfrac{c}{b} = \dfrac{c}{a}$, we simply multiply the reciprocals of $a \div b$ and $b \div c$ together: $(1/2)(4/3) = \boxed{\frac{2}{3}}$.